The director of a training program for a large insurance company is evaluating three different...

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The director of a training program for a large insurance company is evaluating three different methods of training underwriters. The three methods are traditional, CDROM based, and Web based. She divides 30 trainees into three randomly assigned groups of 10. Before the start of the training, each trainee is given a proficiency exam that measures mathematics and computer skills. At the end of the training, all students take the same end-of-training exam. The results, stored in the file underwriting.xls are as follows: Develop a multiple regression model to predict the score on the end-of-training exam, based on the score on the proficiency exam and the method of training used. a. State the multiple regression equation. b. Interpret the meaning of the slopes in this problem. c. Predict the mean end-of-training exam score for a student with a proficiency exam score of 100 who had Web-based training. d. Perform a residual analysis on your results and determine the adequacy of the model. e. Is there a significant relationship between the end-oftraining exam score and the independent variables (proficiency score and training method) at the 0.05 level of significance? f. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data. g. Construct 95% confidence interval estimates of the population slope for the relationship between end-oftraining exam score and each independent variable. h. Interpret the meaning of the coefficient of multiple determination. i. Compute the adjusted r2. j. Compute the coefficients of partial determination and interpret their meaning. k. What assumption about the slope of proficiency score with end-of-training exam score do you need to make in this problem? l. Add interaction terms to the model and, at the 0.05 level of significance, determine whether any interaction terms make a significant contribution to the model. m.On the basis of the results of (f) and (l), which model is most appropriate? Explain.

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Ajay · Accepted Answer

question(a).
Y = b0 + b1X1 + b2X2 + b3X3 + e
The equation for multiple regression looks like this: Y = b0 + b1 X1 + b2 X2 + b3 X3 + e. The slopes of this problem can be broken down as follows
question(b).
The slope for the proficiency score (X1) is the change in the end-of-training exam score (Y) for a one-unit increase in the proficiency score. The slope for the training method (X2) is the difference in the end-of-training exam score (Y) between traditional and CD-ROM based training. The slope for the interaction term (X3) is the difference in (Y) between traditional & Web-based training.
Slope for the proficiency score is determined by the fact that a one-unit improvement in competence results in a commensurate one-unit rise in the end-of-training exam score (Y) (X1). It is possible to determine the slope of a training approach by comparing the final exam results obtained from traditional classroom education with those obtained from instruction based on CD-ROMs (X2). The slope of the interaction term, X3, is equal to the difference in final test scores, Y, that can be attributed to either traditional classroom instruction or study done entirely online.
question(c).
79.3
If a student received instruction that was delivered via the Internet and achieved a perfect 100 on a test of competence, the typical final exam result would be: Y = b0 + b1(100) + b2(1) + b3 (0)= 61.112 + 0.92(100) + 1.115(1) + 0.118 (0)= 79.3
question(d).
The residuals are plotted against the predicted values of the end-of-training exam score. Residuals are randomly distributed.
Residual analysis: There is a comparison made between the projected values of the final exam score and the residuals.

The director of a training program for a large insurance company is evaluating three different methods of training underwriters. The three methods are traditional, CDROM based, and Web based. She...

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